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Design of block backstepping controllers for a class of perturbed multiple inputs and state-delayed systems in semi-strict-feedback form

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  • Yan-Si Lin
  • Chih-Chiang Cheng

Abstract

Based on the Lyapunov stability theorem, an adaptive block backstepping control scheme is proposed in this paper for a class of multi-input systems with mismatched multiple state-delayed perturbations to solve regulation problems. The traditional backstepping control method is modified so that it can be directly applied to systems in block semi-strict-feedback form. The terms in the dynamic equations which do not satisfy the block strict-feedback form are accumulated in the last design step and are suppressed effectively by the adaptive gains, so that the property of asymptotic stability is achieved. Adaptive mechanisms are employed in each of the virtual input controllers as well as the robust controller, hence the least upper bounds of perturbations are not required to be known in advance. A numerical example and a practical application are also given for demonstrating the feasibility of the proposed control scheme.

Suggested Citation

  • Yan-Si Lin & Chih-Chiang Cheng, 2016. "Design of block backstepping controllers for a class of perturbed multiple inputs and state-delayed systems in semi-strict-feedback form," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1296-1311, April.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:6:p:1296-1311
    DOI: 10.1080/00207721.2014.924216
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    References listed on IDEAS

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    1. Ali Koshkouei & Keith Burnham, 2011. "Adaptive backstepping sliding mode control for feedforward uncertain systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(12), pages 1935-1946.
    2. Ching-Hung Lee & Bo-Ren Chung, 2012. "Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(10), pages 1855-1869.
    3. Ruicheng Ma & Jun Zhao & Georgi Dimirovski, 2013. "Backstepping design for global robust stabilisation of switched nonlinear systems in lower triangular form," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(4), pages 615-624.
    4. Tian-Ping Zhang & Qing Zhu & Yue-Quan Yang, 2012. "Adaptive neural control of non-affine pure-feedback non-linear systems with input nonlinearity and perturbed uncertainties," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(4), pages 691-706.
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